如图直线ab与cd相交于点o,od平分∠boe,∠aoe:∠eob=5:4求∠aoc

题目

如图直线ab与cd相交于点o,od平分∠boe,∠aoe:∠eob=5:4求∠aoc

答案

∵∠aoe:∠eob=5:4
∴∠eob=4/9×180
=80°
∠aoe=5/9×180
=100°
又∵od平分∠boe
∴∠doe=1/2∠boe
=1/2×80
=40°
∴∠aoc=∠cod－∠aoe－∠doe
=180－100－40
=40°
答：∠aoc的度数为40°.